수학계를 뒤흔드는 AI: 미해결 난제 속속 풀지만 수학자들의 반응은 엇갈려

AI keeps cracking unsolved math problems, and mathematicians have mixed feelings Matthias Bastian View the LinkedIn Profile of Matthias Bastian Aug 1, 2026 Nano Banana Pro prompted by THE DECODER AI models are cracking conjectures that stumped humans for decades. Reactions in the math community range from shrugs to an existential crisis as the profession grapples with its own possible obsolescence. In May 2026, OpenAI published a counterexample to the "Unit Distance Conjecture," disproving a conjecture in geometric graph theory that had remained open since 1946. It was one of hundreds of open problems linked to Hungarian mathematician Paul Erdos . AI had already helped solve other math problems, including other Erdos problems, but many mathematicians considered this the most significant example yet. Just one week later, human researchers adapted the core proof technique and used it to disprove another major conjecture . Since then, the floodgates have been open, and barely a day goes by without more news about AI in mathematics . Models are finding counterexamples, spotting broader patterns, and helping researchers turn arguments into machine-checkable proofs. Epoch AI, the research group best known for its demanding "FrontierMath" AI benchmark , recently announced the second solution in "FrontierMath: Open Problems," a test drawn from major unsolved questions in math. OpenAI's new Astra model also appears designed for this work: The lab introduced it with ten solutions of varying difficulty. Some mathematicians see a tool, not a threat Abhishek Saha, a math professor at Queen Mary University of London, writes on X , "At the moment, in my area of research mathematics, frontier AI models are at least as good as a solid and indefatigable PhD student." Saha spent a full day using GPT-5.5 Pro for routine work that would previously have taken weeks. The experience left him "increasingly playing the role of conductor, rather than doubling up as the whole orchestra." Saha said most mathematicians don't realize this is already possible, and he expects the field to split over how it responds. "Some will adapt soon, and find boundless possibilities," he wrote. He expects others to resist, adding, "Other academics will continue to be AI-sceptical until the very end, like the folklore hero John Henry." The American folk hero worked himself to death competing against a steam drill. Saha represents a group of researchers who treat AI as a productivity tool rather than an attack on their field. A golden age may not last Writing in The Conversation , mathematician Trefor Bazett says AI and human ingenuity could usher in a new golden age of mathematics. He cites an April 2026 paper from a team of Carnegie Mellon University mathematicians that solved an open problem in Ramsey theory by combining SAT solvers, code generated by language models, and formal proof verification. The paper explicitly connects that result to a "golden age" that Fields Medal winner Timothy Gowers predicted in 2000 . Gowers imagined computers handling routine checks while mathematicians focused on deeper ideas. "In other words, computers would still do the boring bits for us, but these would not be quite as boring as they are now," he wrote. The Carnegie Mellon researchers believe that period has now begun. "We believe that we are now entering this golden age, thanks to the combination of several technologies," they write. But Gowers didn't expect it to last. "However, such a golden age, if it occurs, is unlikely to last for long." He predicted that "during the next century computers will become sufficiently good at proving theorems that the practice of pure mathematical research will be completely revolutionized." Now that his prediction is starting to come true, Gowers has mixed feelings. He says that on two occasions, GPT 5.6 Pro solved a problem on its first attempt after he had spent considerable time working on it. "It felt very strange and not particularly pleasant to have the rug pulled out from under my feet like that," he writes on his blog , though he was still glad to see the problems solved. What worries him most is the "possible destruction of mathematical culture." If fewer people spend years developing deep expertise, he fears the math literature could expand enormously within a decade or two while no human community remains that truly understands it. Gowers raised these concerns in a post about the Leiden Declaration on Artificial Intelligence and Mathematics , an effort to define standards for AI's use in the field. More than 3,000 mathematicians have signed the declaration, which is backed by the International Mathematical Union. Rather than rejecting AI, it calls for transparency when researchers use AI tools, protection of authors' rights, and continued human responsibility for mathematical results. Gowers hasn't signed it, but he broadly supports it. The hardest problems remain out of reach That burst of progress doesn't mean AI can solve everything. According to Bazett, AI performs far better in some areas of math than in others. Fields such as graph theory have proven especially well suited to machine-generated proofs, while others remain resistant. For every problem AI solves, many more remain beyond its reach. Epoch AI's benchmark puts numbers behind those limits. In the two hardest categories, "Major Advance" and "Breakthrough," AI has yet to solve a single problem. The six remaining Millennium Prize Problems , each carrying a $1 million prize from the Clay Mathematics Institute, remain as far out of reach for AI as they are for humans. OpenAI's Astra couldn't solve them either, though OpenAI researcher Noam Brown believes more computing power could change that. Bazett says students who spend years developing their math skills have understandable reasons to worry that AI could replace human researchers. But he adds, "Thankfully, we're not close to that yet." Proof overload could redefine mathematicians' role Mathematician Terence Tao laid out a cautiously optimistic view in his talk at the 2026 International Congress of Mathematicians . He compares the current period to the foundational crisis of the early 20th century, when paradoxes and incompleteness theorems forced mathematicians to reexamine the field's basic assumptions. That crisis ultimately gave mathematics stronger foundations. Tao believes the field is now entering a similarly turbulent period that will force it to rethink its values and working methods. If AI can take over a large share of research tasks, mathematicians can't focus only on solving as many open problems as possible. Proofs must also be checked, explained clearly, understood by other mathematicians, and eventually incorporated into textbooks and broader theories. Tao warns that proof scarcity could give way to proof overload, with results arriving faster than people can review and process them. That would still leave mathematicians with a lasting role. The math community would need to decide which results matter, how they should be presented, and what goals research should pursue. Tao believes answering those questions could leave mathematics stronger and better prepared for future changes. Tao's view of AI has changed over the years. He moved from an initially skeptical position to a pragmatic but still cautious approach to the technology. As early as 2023, he thought reliable and adaptable AI tools were possible. He also predicted that AI could become a reliable coauthor in mathematical research by 2026 . That prediction proved accurate. In October 2025, Tao described how he used ChatGPT in a step-by-step exchange to calculate numerical values for a math problem and write the corresponding Python code. He said it saved him several hours of manual work. Tao sees language models mainly as useful tools that could eventually industrialize mathematics and more complex problems would still require humans and AI to work together . Some mathemat